Mott transition

A Mott transition is a metal-nonmetal transition in condensed matter. Due to electric field screening the potential energy becomes much sharper (exponentially) peaked around the equilibrium position of the atom and electrons become localized and can no longer conduct a current.

Conceptual explanation

In a semiconductor at low temperatures, each 'site' (atom or group of atoms) contains a certain number of electrons and is electrically neutral. For an electron to move away from a site requires a certain amount of energy, as the electron is normally pulled back toward the (now positively charged) site by Coulomb forces. If the temperature is high enough that $\tfrac 1 2 k_B T$ of energy is available per site, the Boltzmann distribution predicts that a significant fraction of electrons will have enough energy to escape their site, leaving an electron hole behind and becoming conduction electrons that conduct current. The result is that at low temperatures a material is insulating, and at high temperatures the material conducts.

The Mott transition is the point in between. Mott argued that the transition must be sudden, occurring when the density of free electrons N and the Bohr radius a_H satisfies $N^{1/3} a_H \simeq 0.2$.

Simply, Mott Transition is changes of materials’ behavior from insulating to metallic due to various factors. This transition is known to exist in various systems: mercury metal Vapor-Liquid, metal NH3 solutions, transition metal chalcogenides and transition metal oxides.^[1] Specifically for transition metal oxides, it has electrical properties from good insulator to good conductor. Especially when it has an intermediate behavior that allows insulator-metal transition in changing T, P or doping. As observed by Mott in his 1949 publication on Ni-oxide. In Mott’s publication, he mentioned the origin of this behavior is from correlations between electrons and its close relationship to magnetism.

For example, when atoms get closer together in solid, electronic state levels broaden and hybridize. At certain critical distance as they draw closer and closer, there is a point where the bands overlap and the originally insulating materials becomes a metallic one. This can be considered a classic Mott transition from insulator to metal by means of pressure.

In semiconductor, the doping level also affects Mott transition. It is observed that higher doping in semiconductor creates internal stress of increasing free energy (acting as a pressure) of the system,^[2] thus reducing the ionization energy as shown by figure below (www.ecse.rpi.edu):

The reduced barrier causes ease of transfer by tunneling or by thermal emission from donor to its adjacent donor. The effect is enhanced when pressure is applied with reason as stated previously. When the transport of carrier reaches minute activation energy, the semiconductor has undergone Mott transition to become metallic.

Other examples of metal-insulator transition include:

• A Mott-Hubbard transition. Ti-doped V₂O₃ undergoes a transition from antiferromagnetic insulator to disordered magnetic conducting state.
• A band crossing transition. EuO orders ferromagnetically from a paramagnetic semiconducting state on cooling below its Curie temperature. Below T_c, europium’s valence electrons have enough energy to cross the trap levels due to vacancies on the oxygen sites. This transfer of electrons transform EuO into metallic state.^[3]
• The Mott transition in doped semiconductors, e.g., Si:P, Si:As, Si:B, Si:Ga, etc. Such transitions have been effectively investigated and demonstrated using electronic Raman scattering.^[4]

History

The theory was first proposed by Nevill Francis Mott in a 1949 paper.^[5] Mott also wrote a review of the subject (with a good overview) in 1968.^[6]

Notes

1. ^ Cyrot, M (1972). "Theory of mott transition : Applications to transition metal oxides". Le Journal de Physique 33 (125). 
2. ^ Bose, D. N.; B. Seishu, G. Parthasarathy and E. S. R. Gopal (1986). "Doping Dependence of Semiconductor-Metal Transition in InP at High Pressures". Proceedings of the Royal Society of London: A 405 (1829). JSTOR 2397982. 
3. ^ Michel Schlenker; Etienne du Trémolet de Lacheisserie; Du Trڳemolet de Lacheisserie, Etienne; Du Trémolet de Lacheisserie, Etienne; Damien Gignoux (2005). Magnetism. Berlin: Springer. ISBN 0-387-22967-1. 
4. ^ Jain, K., et al., Electronic Raman scattering and the metal-insulator transition in doped silicon, Phys. Rev. B, Vol. 13, 5448 (1976).
5. ^ N. F. Mott, Proc. Phys. Soc. (London) A62, 416 (1949)
6. ^ N. F. Mott, Rev. Mod. Phys, 40, pp677--683.